1. Technical Field of the Invention
The present invention relates to a method for combining partially measured data obtained from measurements taken on a large number of places on a free form surface by joining the measured data together.
2. Prior Art
When the surface of an object is so wide that the entire surface cannot be measured in one operation, such as when measuring the geometrical data of the surface of an automobile mock-up model, a three-dimensional coordinate measuring machine (digitizer) is used to measure sections of the surface of the object which partially overlap each other, and the measured data for the parts are combined together (stitched).
More explicitly, when using no contact measuring instrument such as an aperture interferometer or range finder, if the total Information about an object cannot be obtained in one measuring operation, the sensor or the object being measured is translated and rotated in three-dimensional space, the partially measured data (the set of measurement points obtained from the sensor at one location) are collected and then processed numerically, and he three-dimensional shape information about the object is reconstructed.
In general, xe2x80x9cmeasurementxe2x80x9d means determining the accuracy by comparing the data to some ideal reference information such as design data, and xe2x80x9cdigitizingxe2x80x9d is used for the case in which no such reference information is used. Typically, obtaining a numerical data of a natural object or an industrial design (for instance, the clay model of an automobile) means xe2x80x9cdigitizing.xe2x80x9d In other words, both measurement and digitizing mean that a set of three-dimensional coordinate information is obtained using any type of sensor at sufficiently close intervals that details of the information can be reproduced in a computer; the systems are called xe2x80x9cmeasuring instrumentxe2x80x9d and xe2x80x9cdigitizerxe2x80x9d for the former and the latter, respectively.
The present invention, according to the aforementioned definition, relates to xe2x80x9cdigitizingxe2x80x9d without reference to other information concerning the object being measured (design drawings such as CAD data). However, both digitizing and measurement are generally called xe2x80x9cmeasurementxe2x80x9d in the following paragraphs. In addition, the object being measured is assumed to be a continuous body without holes or discontinuities. Furthermore, the partially measured data must overlap and be measured or digitized.
Conventional methods for combining or registration of such data measured in parts, known in the prior art, include the simple combination method and the fitting combination (registration) method. In the simple combination method, partial surfaces are combined relying only on the accuracy of determining the position of the stage. However, there is the problem of low accuracy due to the introduction of Abbe""s error. The fitting combination method adjusts the positions and angles of the partial surfaces so that the parts of the partial surfaces which overlap each other are overlapped as smoothly as possible. However, this method has the problem that errors accumulate in proportion to the {fraction (3/2)} power of the number of combination cycles.
Methods for solving these problems include one in which two part al surfaces are first overlapped, and then other partial surfaces are added to the overlapped one, one after another, as disclosed in xe2x80x9cStudy on registration of range imagesxe2x80x9d (by Ikuko Shimizu, Doctorate Thesis, Tokyo University).
According to this combination method, however, when combining N sets of partially measured data, the N-th set overlaps (Nxe2x88x921)-th sets that have been combined together, and then, to avoid cumulative errors, the coordinates of the data that have already been overlapped must be transformed again. As a consequence, to combine N sets of partially measured data, the coordinates must be transformed 1+2+ . . . +N=(1+N) N/2 times, that is, this method has the problem that the data processing time increases in proportion to substantially the square of the number N of sets of data to be combined.
Another proposed method is the xe2x80x9cShape measuring methods and apparatusxe2x80x9d (unexamined Japanese patent publication No. 160428, 1998). This method combines the fitting combination method for fitting and connecting data in the normal directions of the overlapping surfaces only with the simple combination method in which coordinates are directly transferred, trusting on information from the machine.
The advantage of this method is its capability for combining quickly and very precisely, despite a rather simple procedure. In detail, the partial data are combined in one direction (straight or zigzag), and the fitting combination method is applied only in one direction at each step, so the total data processing time is substantially proportional to the number, N, of sets being combined.
However, because the fitting combination method is applied only In one direction in this method, only forward and backward continuity is taken into account. Therefore although no cumulate errors are produced, there is the problem that continuity in the transverse direction cannot be included. In addition, by considering fitting only in the normal direction, measurement errors for the other five components (two translational components and three rotational components) are ignored under the assumption that the measurement errors will be distributed evenly. However, the errors may not be negligible depending on the characteristics of the measuring instrument or digitizer, so the problem with this method is low analysis accuracy.
The present invention is aimed at solving these problems. More explicitly, an object of the present invention is to provide a method of combining partially measured data whereby highly accurate combined data can be created from a plurality of sets of partially measured data, using a small number of iterative calculations.
The present invention provides a method of combining partially measured data, wherein (A) the surface shape of an object (1) is measured by changing locations and/or directions, and a plurality of sets of partially measured data (2) including the common parts (2a) are collected, (B) the ranges (3a) over which adjacent common parts (2a) are overlapped in the measurement error ranges (3) are determined for all partially measured data (2), (C) if there are no ranges (3a) where the parts are overlapped, combining is judged to be impossible, and (D) when there are ranges in which the parts (3a) are overlapped, the common parts of each set of partially measured data are combined over the overlapped ranges (3a).
According to this method, because the ranges (3a) in which adjacent common parts (2a) are overlapped are determined in the measurement error ranges (3) for all sets of partially measured data (2), as described in the above-mentioned (B), whether or not overlapped ranges (3a) exist can be determined very rapidly. When there are no overlapped ranges (3a), the measurement data contain errors that are larger than the expected measurement error by design specification. Therefore, if iterative calculations are made for the combination, no solution can be ultimately obtained. Therefore, time-consuming repetitive computations can be avoided by mating a judgment to enable comb nation in case (C) in which there are no overlapped ranges (3a).
In addition, even when there are overlapped ranges (3a) in the aforementioned (D), the common parts of each set of partially measured data are combined only in the overlapped ranges of the measurement error ranges (3). Therefore, the ranges over which the coordinates of the data are transformed during combination are so narrow that wasteful iterated calculations can be minimized.
Moreover, since the common parts of each partially measured data are-combined sequentially using four fixed ranges (3a) of measurement error ranges (3), when N sets of partially measured data are combined, no errors accumulate, so it is unnecessary to re-transform the coordinates of the data which have already been overlapped. As a result, N coordinate transformations are sufficient to combine N sets of partially measured data. Therefore, combining can be completed in a processing time substantially proportional to the number of sets N being combined.
According to a preferred embodiment of the present invention, in the above-mentioned (D), (E) the coordinates of each set of partially measured data are transformed so that the position data for a group of common parts (2a) fall within the overlapped ranges (3a), (F) next, the common parts (2a) of each set of partially measured data are combined while the common parts still remain in the overlapped ranges (3a) even after the coordinates have been transformed.
According to the aforementioned methods, only the group of position data for the common parts (2a) in the overlapped ranges (3a) has its coordinates transformed, therefore the ranges over which the coordinates of the data are transformed during combination are narrow and the amount of position data is small, so that the calculation time can be reduced.
Furthermore, since the common parts are combined while the common parts (2a) of each set of partially measured data still remain in the overlapped ranges (3a) even after the coordinates have been transformed, no errors accumulate and the coordinates of the whole of the partially measured data can be transformed quickly.